CN111553734A - Method and system for predicting marketing decision result - Google Patents

Abstract

The invention discloses a method and a system for predicting marketing decision results, wherein the method comprises the following steps: obtaining influence factors, wherein the influence factors comprise key influence factors, obtaining random factors capable of influencing the key influence factors, calculating results related to marketing decisions based on the random factors and the influence factors, and obtaining n different final prediction results and distribution thereof through n Monte Carlo simulations and calculation according to the same input information. In the prediction process, the accuracy of the marketing decision result prediction is effectively improved by adding the random factor.

Description

Method and system for predicting marketing decision result

Technical Field

The invention relates to the technical field of data processing, in particular to a method and a system for predicting a marketing decision result.

Background

Enterprises need to win customers for themselves through marketing campaigns to gain profits, and when marketing campaigns are performed, the feasibility of the marketing campaigns is often analyzed by predicting the cost and future benefits required by the campaigns. When a manager or a financial staff uses a BI (Business Intelligence, a sum of a series of methods, technologies and software adopted for improving the Business operation performance) analysis tool or a financial budget decision method to predict the income of future activities by using historical data, the interference of some random factors on the result is rarely considered or not considered, and finally one or a plurality of possible results are obtained to support the decision. The random factor affects the key variable that affects future results, causing the actual value of the key variable to deviate from the initial estimated value.

Therefore, how to effectively improve the accuracy of the marketing decision result prediction is an urgent problem to be solved.

Disclosure of Invention

In view of the above, the invention provides a method for predicting a marketing decision result, and in the prediction process, by adding a random factor, the accuracy of the marketing decision result prediction is effectively improved.

The invention provides a method for predicting marketing decision results, which comprises the following steps:

acquiring influence factors, wherein the influence factors comprise key influence factors;

acquiring a random factor capable of influencing the key influence factor;

calculating a result related to a marketing decision based on the random factor and the impact factor;

and obtaining n different final prediction results and the distribution thereof through n Monte Carlo simulations and calculation according to the same input information.

Preferably, the obtaining a random factor capable of affecting the key impact factor includes:

and respectively obtaining a random factor capable of influencing the life cycle length of the customer, a random factor of the customer loss rate, a random factor of the number of customers acquired by the marketing campaign and a random factor of the conversion rate of the marketing campaign.

Preferably, the obtaining the influence factor includes:

obtaining customer-related data, marketing campaign data, and a profit adjustment factor, wherein the customer-related data comprises: the service life of the client is prolonged, the annual transaction frequency of the client, the transaction amount of the client each time, the loss rate of the client, the annual maintenance cost of the client and the number of the clients obtaining the marketing campaign are reduced; the marketing campaign data comprises: marketing campaign conversion rate, campaign budget, and advertisement placement cost; the profit adjustment factor includes: and (4) discount rate.

Preferably, the calculating a result related to marketing decision based on the random factor and the influence factor comprises:

calculating an intermediate result based on the random factor and the impact factor, wherein the intermediate result comprises: the amount of the client left in stock per year, the amount of the client consumed per year and the profit per year;

calculating a result related to a marketing decision based on the intermediate result, wherein the result related to the marketing decision comprises: lifetime value of the customer, customer acquisition cost and average net profit and loss.

A system for predicting marketing decision outcomes, comprising:

the device comprises a first acquisition module, a second acquisition module and a control module, wherein the first acquisition module is used for acquiring influence factors, and the influence factors comprise key influence factors;

the second acquisition module is used for acquiring random factors capable of influencing the key influence factors;

a calculation module for calculating a result related to a marketing decision based on the random factor and the impact factor;

and the Monte Carlo simulation module is used for obtaining n different final prediction results and the distribution thereof through n Monte Carlo simulations and calculation according to the same input information.

Preferably, the second obtaining module is specifically configured to:

and respectively obtaining a random factor capable of influencing the life cycle length of the customer, a random factor of the customer loss rate, a random factor of the number of customers acquired by the marketing campaign and a random factor of the conversion rate of the marketing campaign.

Preferably, the first obtaining module is specifically configured to:

obtaining customer-related data, marketing campaign data, and a profit adjustment factor, wherein the customer-related data comprises: the service life of the client is prolonged, the annual transaction frequency of the client, the transaction amount of the client each time, the loss rate of the client, the annual maintenance cost of the client and the number of the clients obtaining the marketing campaign are reduced; the marketing campaign data comprises: marketing campaign conversion rate, campaign budget, and advertisement placement cost; the profit adjustment factor includes: and (4) discount rate.

Preferably, the calculation module is specifically configured to:

calculating an intermediate result based on the random factor and the impact factor, wherein the intermediate result comprises: the amount of the client left in stock per year, the amount of the client consumed per year and the profit per year;

calculating a result related to a marketing decision based on the intermediate result, wherein the result related to the marketing decision comprises: lifetime value of the customer, customer acquisition cost and average net profit and loss.

In summary, the present invention discloses a method for predicting a marketing decision result, when a marketing decision result needs to be predicted, first obtaining an influence factor, wherein the influence factor includes a key influence factor, then obtaining a random factor, which can influence the key influence factor, of a random factor, which can influence the influence factor, and then calculating a result related to the marketing decision based on the random factor and the influence factor; and obtaining n different final prediction results and the distribution thereof through n Monte Carlo simulations and calculation according to the same input information. According to the invention, random factors are added into the key influence factors, a Monte Carlo method is used for testing, and possible results are finally obtained according to the test times, so that the predicted results can be more comprehensively and visually reflected, and the defects in the prior art are overcome; the introduced random factors can more accurately simulate the change track of the affected elements in the future, and the accidental events can be simulated in a certain experiment in the simulation experiment, so that the result is more comprehensive and accurate.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

Fig. 1 is a flowchart of a method of predicting a marketing decision result according to an embodiment 1 of the present invention;

FIG. 2 is a flowchart of a method of predicting marketing decision results in accordance with embodiment 2 of the present invention;

FIG. 3 is a schematic structural diagram of an embodiment 1 of a system for predicting marketing decision results according to the present disclosure;

fig. 4 is a schematic structural diagram of a system for predicting a marketing decision result according to an embodiment 2 of the present disclosure.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

As shown in fig. 1, which is a flowchart of a method of embodiment 1 of the method for predicting a marketing decision result disclosed in the present invention, the method may include the following steps:

s101, obtaining influence factors, wherein the influence factors comprise key influence factors;

when the result of the marketing decision needs to be predicted, firstly, according to the actual prediction requirement, the influence factor which influences the final prediction result is obtained. The influence factors include key influence factors which are easy to interfere and then fluctuate.

S102, acquiring a random factor capable of influencing a key influence factor;

for the obtained key influence factors, by analyzing the rough distribution of the key influence factors, the factors with influenced distribution, namely, random factors, are obtained.

S103, calculating a result related to marketing decision based on the random factor and the influence factor;

and after the influence factors and the random factors capable of influencing the influence factors are obtained, further calculating results related to marketing decisions according to the random factors and the influence factors.

And S104, obtaining n different final prediction results and distribution thereof through n Monte Carlo simulations and calculation according to the same input information.

And finally, carrying out a test by using a Monte Carlo method, carrying out multiple Monte Carlo simulations, obtaining multiple different final prediction results and distribution thereof through calculation according to the same input information, and further guiding the optimal allocation of key resources of the enterprise according to the output results. The test times n can be flexibly set according to actual prediction requirements.

In summary, in the above embodiment, when the result of the marketing decision needs to be predicted, the impact factor is obtained first, where the impact factor includes a key impact factor, then the random factor capable of affecting the key impact factor and capable of affecting the impact factor is obtained, and then the result related to the marketing decision is calculated based on the random factor and the impact factor; and obtaining n different final prediction results and the distribution thereof through n Monte Carlo simulations and calculation according to the same input information. According to the invention, random factors are added into the key influence factors, a Monte Carlo method is used for testing, and possible results are finally obtained according to the test times, so that the predicted results can be more comprehensively and visually reflected, and the defects in the prior art are overcome; the introduced random factors can more accurately simulate the change track of the affected elements in the future, and the accidental events can be simulated in a certain experiment in the simulation experiment, so that the result is more comprehensive and accurate.

As shown in fig. 2, which is a flowchart of a method of embodiment 2 of the method for predicting a marketing decision result disclosed in the present invention, the method may include the following steps:

s201, obtaining client related data, marketing activity data and profit adjustment factors, wherein the client related data comprises: the service life of the client is prolonged, the annual transaction frequency of the client, the transaction amount of the client each time, the loss rate of the client, the annual maintenance cost of the client and the number of the clients obtaining the marketing campaign are reduced; the marketing campaign data comprises: marketing campaign conversion rate, campaign budget, and advertisement placement cost; the profit adjustment factor includes: the discount rate;

when the result of the marketing decision needs to be predicted, firstly, according to the actual prediction demand, obtaining influence factors which have influence on the final prediction result, such as the customer life cycle length, the annual transaction times TN of the customer, the transaction amount (product unit price) P of the customer, the customer attrition rate, the annual maintenance cost RC of the customer, the number of customers obtained in the marketing campaign, the transformation rate of the marketing campaign, the campaign budget, the advertisement putting cost and the discount rate DR.

S202, respectively obtaining a random factor capable of influencing the life cycle length of a customer, a random factor of customer attrition rate, a random factor of the number of customers acquired in a marketing campaign, and a random factor of the conversion rate of the marketing campaign;

then, a random factor that can affect the key influencing factor is obtained. That is, for a key future-varying influence factor, it is assumed that it follows a certain distribution according to its characteristics, and a parameter that affects the distribution is determined. For example, the key impact factors affected by the random factor are (are random values subject to respective expressions):

(1) customer lifecycle length (>0), assuming it follows a normal distribution, and LT > 0;

(2) customer churn rate: LR ═ r, (0< r <1), there will be customer churn each year that the marketing campaign gets, no longer purchasing products from the enterprise, assuming customer churn occurs at early years.

(3) Marketing campaign conversion MCR (>0), assuming it follows a normal distribution;

(4) marketing campaign number of acquaintances MCN, which obeys two distributions:

wherein, p is the probability that the advertisement can be converted into the customer, namely the conversion rate MCR. The test times n are different customers who are put in the marketing campaign and equal to the campaign budget S/single advertisement putting cost C.

S203, calculating an intermediate result based on the random factor and the influence factor, wherein the intermediate result comprises: the amount of the client left in stock per year, the amount of the client consumed per year and the profit per year; after the influence factors and the random factors capable of influencing the influence factors are obtained, the result related to the marketing decision is further calculated according to the random factors and the influence factors,

then it is calculated that within a certain customer lifetime LT:

the annual customer reserve CL ═ CL (CL)₁，cl₂,…,cl_n),n＝LT，

cl_i＝cl_i-1*MCN*(1-LR)；

The amount SP (SP) consumed by the client each year₁,sp₂,…,sp_n),n＝LT，

sp_i＝cl_i*TN*P；

Annual profit PF (PF)₁,pf₂,…,pf_n),n＝LT，

pf_i＝cl_i*(TN*P-RC)；

Wherein 1 ≦ i ≦ LT, and when i ≦ 1, cl_i-1＝1。

S204, calculating a result related to the marketing decision based on the intermediate result, wherein the result related to the marketing decision comprises: the lifetime value of the customer, the customer acquisition cost and the average net profit and loss;

from a financial perspective, due to the time value of currency, future benefits need to be discounted in order to more accurately measure the value of the future benefits at the current time. The current value PV ═ PV of annual profit₁,pv₂,…，pv_n) N is LT, wherein pv_i＝pf_i*(1+DR)^-i；

And finally, obtaining a needed decision result for a single client:

life-long value of customer

The customer obtains the cost CAC ═ S/MCN;

the average net profit AVPF is CLTV-CAC.

S205, obtaining n different final prediction results and distribution thereof through n Monte Carlo simulations and calculation according to the same input information.

And finally, carrying out a test by using a Monte Carlo method, carrying out multiple Monte Carlo simulations, obtaining multiple different final prediction results and distribution thereof through calculation according to the same input information, and further guiding the optimal allocation of key resources of the enterprise according to the output results. The test times n can be flexibly set according to actual prediction requirements. That is, repeating the calculation n times to obtain the variable affected by the random factor, and outputting the final n CLTV, CAC, AVPF results and the distribution diagram.

In conclusion, the process of future marketing activities can be simulated automatically by inputting random factors and other influence factors which influence key influence factors, and the final life value and the acquisition cost of customers are obtained according to the set test times, so that more scientific support is provided for decision making; by adjusting the determined influence factors, such as marketing activity budget, product unit price, customer maintenance cost and the like, the output variables are updated accordingly, so that decision results under different conditions can be simulated, and decision balancing between input and output results is realized; the range of certain impact factors can be deduced according to the ideal final result, so as to guide the optimal allocation of key resources (such as manpower, budget and the like) of the enterprise.

As shown in fig. 3, which is a schematic structural diagram of an embodiment 1 of the system for predicting a marketing decision result disclosed in the present invention, the system may include:

a first obtaining module 301, configured to obtain an influence factor, where the influence factor includes a key influence factor;

when the result of the marketing decision needs to be predicted, firstly, according to the actual prediction requirement, the influence factor which influences the final prediction result is obtained. The influence factors include key influence factors which are easy to interfere and then fluctuate.

A second obtaining module 302, configured to obtain a random factor that can affect the key impact factor;

for the obtained key influence factors, by analyzing the rough distribution of the key influence factors, the factors with influenced distribution, namely, random factors, are obtained.

The monte carlo simulation module 304 is configured to obtain n different final prediction results and distributions thereof through n monte carlo simulations and according to the same input information through calculation.

And finally, carrying out a test by using a Monte Carlo method, carrying out multiple Monte Carlo simulations, obtaining multiple different final prediction results and distribution thereof through calculation according to the same input information, and further guiding the optimal allocation of key resources of the enterprise according to the output results. The test times n can be flexibly set according to actual prediction requirements.

In summary, in the above embodiment, when the result of the marketing decision needs to be predicted, the impact factor is obtained first, where the impact factor includes a key impact factor, then the random factor capable of affecting the key impact factor and capable of affecting the impact factor is obtained, and then the result related to the marketing decision is calculated based on the random factor and the impact factor; and obtaining n different final prediction results and the distribution thereof through n Monte Carlo simulations and calculation according to the same input information. According to the invention, random factors are added into the key influence factors, a Monte Carlo method is used for testing, and possible results are finally obtained according to the test times, so that the predicted results can be more comprehensively and visually reflected, and the defects in the prior art are overcome; the introduced random factors can more accurately simulate the change track of the affected elements in the future, and the accidental events can be simulated in a certain experiment in the simulation experiment, so that the result is more comprehensive and accurate.

As shown in fig. 4, which is a schematic structural diagram of embodiment 2 of the system for predicting a marketing decision result disclosed in the present invention, the system may include:

a first obtaining module 401, configured to obtain customer-related data, marketing campaign data, and profit adjustment factors, wherein the customer-related data includes: the service life of the client is prolonged, the annual transaction frequency of the client, the transaction amount of the client each time, the loss rate of the client, the annual maintenance cost of the client and the number of the clients obtaining the marketing campaign are reduced; the marketing campaign data comprises: marketing campaign conversion rate, campaign budget, and advertisement placement cost; the profit adjustment factor includes: the discount rate;

when the result of the marketing decision needs to be predicted, firstly, according to the actual prediction demand, obtaining influence factors which have influence on the final prediction result, such as the customer life cycle length, the annual transaction times TN of the customer, the transaction amount (product unit price) P of the customer, the customer attrition rate, the annual maintenance cost RC of the customer, the number of customers obtained in the marketing campaign, the transformation rate of the marketing campaign, the campaign budget, the advertisement putting cost and the discount rate DR.

A second obtaining module 402, configured to obtain a random factor that can affect a life cycle length of a customer, a random factor of a customer churn rate, a random factor of a number of customers acquired in a marketing campaign, and a random factor of a conversion rate of the marketing campaign, respectively;

then, a random factor that can affect the key influencing factor is obtained. That is, for a key future-varying influence factor, it is assumed that it follows a certain distribution according to its characteristics, and a parameter that affects the distribution is determined. For example, the key impact factors affected by the random factor are (are random values subject to respective expressions):

(1) customer lifecycle length (>0), assuming it follows a normal distribution, and LT > 0;

(2) customer churn rate: LR ═ r, (0< r <1), there will be customer churn each year that the marketing campaign gets, no longer purchasing products from the enterprise, assuming customer churn occurs at early years.

(3) Marketing campaign conversion MCR (>0), assuming it follows a normal distribution;

(4) marketing campaign number of acquaintances MCN, which obeys two distributions:

wherein, p is the probability that the advertisement can be converted into the customer, namely the conversion rate MCR. The test times n are different customers who are put in the marketing campaign and equal to the campaign budget S/single advertisement putting cost C.

A calculating module 403, configured to calculate an intermediate result based on the random factor and the influence factor, where the intermediate result includes: the amount of the client left in stock per year, the amount of the client consumed per year and the profit per year;

after the influence factors and the random factors capable of influencing the influence factors are obtained, further calculating results related to marketing decisions according to the random factors and the influence factors, and then calculating the results within a determined customer life cycle LT:

the annual customer reserve CL ═ CL (CL)₁,cl₂,…,cl_n)，n＝LT，

cl_i＝cl_i-1*MCN*(1-LR)；

The amount SP (SP) consumed by the client each year₁，sp₂，…，sp_n),n＝LT，

sp_i＝cl_i*TN*P；

Annual profit PF (PF)₁,pf₂,…,pf_n)，n＝LT，

pf_i＝cl_i*(TN*P-RC)；

Wherein 1 ≦ i ≦ LT, and when i ≦ 1, cl_i-1＝1。

The calculating module 403 is further configured to calculate a result related to the marketing decision based on the intermediate result, where the result related to the marketing decision includes: the lifetime value of the customer, the customer acquisition cost and the average net profit and loss;

from a financial perspective, due to the time value of currency, future benefits need to be discounted in order to more accurately measure the value of the future benefits at the current time. The current value PV ═ PV of annual profit₁，pv₂，…，pv_n) N is LT, wherein pv_i＝pf_i*(1+DR)^-i；

And finally, obtaining a needed decision result for a single client:

life-long value of customer

The customer obtains the cost CAC ═ S/MCN;

the average net profit AVPF is CLTV-CAC.

A monte carlo simulation module 404, configured to obtain n different final prediction results and distributions thereof through n monte carlo simulations and according to the same input information through calculation.

And finally, carrying out a test by using a Monte Carlo method, carrying out multiple Monte Carlo simulations, obtaining multiple different final prediction results and distribution thereof through calculation according to the same input information, and further guiding the optimal allocation of key resources of the enterprise according to the output results. The test times n can be flexibly set according to actual prediction requirements. That is, repeating the calculation n times to obtain the variable affected by the random factor, and outputting the final n CLTV, CAC, AVPF results and the distribution diagram.

In conclusion, the process of future marketing activities can be simulated automatically by inputting random factors and other influence factors which influence key influence factors, and the final life value and the acquisition cost of customers are obtained according to the set test times, so that more scientific support is provided for decision making; by adjusting the determined influence factors, such as marketing activity budget, product unit price, customer maintenance cost and the like, the output variables are updated accordingly, so that decision results under different conditions can be simulated, and decision balancing between input and output results is realized; the range of certain impact factors can be deduced according to the ideal final result, so as to guide the optimal allocation of key resources (such as manpower, budget and the like) of the enterprise.

The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.

Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.

The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (8)

1. A method of predicting marketing decision results, comprising:

acquiring influence factors, wherein the influence factors comprise key influence factors;

acquiring a random factor capable of influencing the key influence factor;

calculating a result related to a marketing decision based on the random factor and the impact factor;

and obtaining n different final prediction results and the distribution thereof through n Monte Carlo simulations and calculation according to the same input information.

2. The method of claim 1, wherein obtaining a random factor that can affect the key impact factor comprises:

and respectively obtaining a random factor capable of influencing the life cycle length of the customer, a random factor of the customer loss rate, a random factor of the number of customers acquired by the marketing campaign and a random factor of the conversion rate of the marketing campaign.

3. The method of claim 2, wherein the obtaining the impact factors comprises:

obtaining customer-related data, marketing campaign data, and a profit adjustment factor, wherein the customer-related data comprises: the service life of the client is prolonged, the annual transaction frequency of the client, the transaction amount of the client each time, the loss rate of the client, the annual maintenance cost of the client and the number of the clients obtaining the marketing campaign are reduced; the marketing campaign data comprises: marketing campaign conversion rate, campaign budget, and advertisement placement cost; the profit adjustment factor includes: and (4) discount rate.

4. The method of claim 3, wherein computing a result related to a marketing decision based on the stochastic factor and the impact factor comprises:

calculating an intermediate result based on the random factor and the impact factor, wherein the intermediate result comprises: the amount of the client left in stock per year, the amount of the client consumed per year and the profit per year;

calculating a result related to a marketing decision based on the intermediate result, wherein the result related to the marketing decision comprises: lifetime value of the customer, customer acquisition cost and average net profit and loss.

5. A system for predicting marketing decision results, comprising:

the device comprises a first acquisition module, a second acquisition module and a control module, wherein the first acquisition module is used for acquiring influence factors, and the influence factors comprise key influence factors;

the second acquisition module is used for acquiring random factors capable of influencing the key influence factors;

a calculation module for calculating a result related to a marketing decision based on the random factor and the impact factor;

and the Monte Carlo simulation module is used for obtaining n different final prediction results and the distribution thereof through n Monte Carlo simulations and calculation according to the same input information.

6. The system of claim 5, wherein the second obtaining module is specifically configured to:

and respectively obtaining a random factor capable of influencing the life cycle length of the customer, a random factor of the customer loss rate, a random factor of the number of customers acquired by the marketing campaign and a random factor of the conversion rate of the marketing campaign.

7. The system of claim 6, wherein the first obtaining module is specifically configured to:

obtaining customer-related data, marketing campaign data, and a profit adjustment factor, wherein the customer-related data comprises: the service life of the client is prolonged, the annual transaction frequency of the client, the transaction amount of the client each time, the loss rate of the client, the annual maintenance cost of the client and the number of the clients obtaining the marketing campaign are reduced; the marketing campaign data comprises: marketing campaign conversion rate, campaign budget, and advertisement placement cost; the profit adjustment factor includes: and (4) discount rate.

8. The system of claim 7, wherein the computing module is specifically configured to:

calculating an intermediate result based on the random factor and the impact factor, wherein the intermediate result comprises: the amount of the client left in stock per year, the amount of the client consumed per year and the profit per year;

calculating a result related to a marketing decision based on the intermediate result, wherein the result related to the marketing decision comprises: lifetime value of the customer, customer acquisition cost and average net profit and loss.

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